There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Tables of integrals

The Convolution Transform. By Hirschmann & Widder . Pp. x + 268. 45s. 1955. (Princeton University Press. London : Cumberlege)

The Of Economic Dynamics

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http://pcmap.unizar.es/~chelo/investig/publicaciones/chelo/Hurwitz-Lerch/original.pdf

Asymptotic expansions of the Hurwitz–Lerch zeta function

http://pcmap.unizar.es/~chelo/investig/publicaciones/joseluis/doublegamma.pdf

An Asymptotic Expansion of the Double Gamma Function

http://pcmap.unizar.es/~chelo/investig/publicaciones/chelo/Incomplete%20gamma/AAM05.pdf

Incomplete gamma functions for large values of their variables

Asymptotic expansions of Stieltjes and generalized Stieltjes transforms of functions having an asymptotic expansion in negative integer powers of their variable have been exhaustively investigated by R. Wong. In this article, we extend this analysis to Stieltjes and generalized Stieltjes transforms of functions having an asymptotic expansion in negative rational powers of their variable. Distributional approach is used to derive asymptotic expansions of the Stieltjes and generalized Stieltjes transforms of this kind of functions for large values of the parameter(s) of the transformation. Error bounds are obtained at any order of the approximation for a large family of integrands. The asymptotic approximation of an integral involved in the calculation of the mass renormalization of the quantum scalar field and of the third symmetric elliptic integral are given as illustrations.

Chelo Ferreira

Papers

Asymptotic expansions of the Hurwitz–Lerch zeta function

An Asymptotic Expansion of the Double Gamma Function

Incomplete gamma functions for large values of their variables

Asymptotic Expansions of Generalized Stieltjes Transforms of Algebraically Decaying Functions

New method to estimate the sample size for calculation of a proportion assuming binomial distribution.